An improved type-reduction algorithm for general type-2 fuzzy sets

Abstract

General type-2 fuzzy systems (GT2 FLSs) provide a more flexible way of overcoming an uncertain lack of uniformity in different applications. Centroid type reduction is one of the major component of GT2 FLSs, it is currently one of the key factors restricting GT2 FLSs efficiency. This paper proposes a novel and efficient method for centroid type reduction. The method is based on α-plane representation, where a general type-2 fuzzy set is decomposing into a series of α planes. The centroid for each plane is the calculated, layer by layer, from the top down, until the α=0 plane is reached. In each α plane, a centroid type reduction calculation is performed using an improved enhanced opposite direction searching algorithm (IEODS). Finally, the centroids obtained for each plane are aggregated to obtain a type-1 fuzzy set, which form the centroid of general type-2 fuzzy set. Experiments show that this method results in less calculation time and fewer iterations than other α-plane representation-based reduction methods. By providing more efficient type reduction, the method improves the applicability of general type-2 fuzzy systems in more complex environments and embedded platforms, thereby enhancing their scope for future development.